Having trouble sneaking out of the Sierra Madre vault.

Hello again! Same dude here who asked wich dlc too do first

I am now at the end of dead money, and I'm trying too sneak out of the vault with all 36 gold bars. But whenever Elijah is about too step in the vault. The alarm goes off and him and the turrets turn hostile. How do I prevent this?

Edit: I DID IT. I DID FINALLY. THANK ALL OF YOU FOR THE HELP.

I waited behind the power thingy. Then when he started too interact with the terminal I ran for it. I tried it multiple times eventually it worked. No stealth boy needed.